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ISSN: 2332-2519
Journal of Astrobiology & Outreach
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Energy of Spinning Black Holes in XRBs and AGN

Dipo Mahto1*, Md Shams Nadeem2, Umakant Prasad3 & Kumari Vineeta4
1Assistant Professor, Dept. of Physics, Marwari College,T.M.B.U.Bhagalpur-812007, India
2Research Scholar, University Dept. of Physics, T. M. B. U. Bhagalpur- 812007, India
3Assistant Professor, Dept. of Physics, T.N.B. College,T. M. B. U. Bhagalpur-812007,India
4Lecturer in Physics, Dept. of Education, S.M. College,T.M.B.U.Bhagalpur-812007, India
Corresponding Author : Dipo Mahto
Assistant Professor, Department of Physics
Marwari College, T.M.B.U. Bhagalpur-812007, India
Tel: 91 141 277 108
E-mail: [email protected]
Received March 17, 2014; Accepted April 22, 2014; Published April 24, 2014
Citation: Mahto D, Nadeem MS, Prasad U, Vineeta K (2014) Energy of Spinning Black Holes in XRBs and AGN. Astrobiol Outreach 2:109. doi:10.4172/2332-2519.1000109
Copyright: © 2014 Mahto D, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Keywords
Event horizon, XRBs, AGN and Energy
Introduction
James Bardeen, Jacob Bekenstein, Carter, and Hawking have vital role to lead the formulation of the laws of black hole mechanics. The laws of black hole mechanics describe the behaviour of a black hole in close analogy to the laws thermodynamics by relating mass to energy, area to entropy, and surface gravity to temperature [1-3]. In October 23, 2001, scientists for the first time have seen energy being extracted from a black hole. Like an electric dynamo, this black hole spins and pumps energy out through cable-like magnetic field lines into the chaotic gas whipping around it, making the gas already internally hot from the sheer force of crushing gravity even hotter [4]. In 2011, Dipo Mahto et al. derived also an expression for the energy of spinning black holes in terms of the radius of event horizon given by the equation where is the black hole constant having the value 1.214×1044 J /m for spinning black holes [5]. In the same year, Dipo Mahto et al. derived an expression for the change in energy and entropy of non-spinning black holes taking account the first law of the black hole mechanics relating the change in mass M, angular momentum J, horizon area A and charge Q, of a stationary black hole with Einstein’s mass-energy equivalence relation [3]. In 2013, Dipo Mahto et al. justified the model for energy of non-spinning black holes as proposed by Kanak Kumari et al. in 2010.
In the present paper, we have calculated the energy of different spinning black holes existing in XRBs and AGN on the basis of this model. The calculation shows that the total energy of the rest masses M ~ 5 -20 of stellar – mass black holes in X-ray binaries is few×1055 ergs and for the masses M ~ 106-109.5. of super massive black holes in active galactic nuclei is few× 1060-1064 ergs.
Expression for the Energy of Spinning Black Hole
In 2005, Ram et al. concluded that the black hole is a Bose-Einstein ensemble of quanta of mass equals to twice the Planck mass, confined in a sphere of radius twice the black hole [6]. Quantum mechanically, however, there is a possibility that one of a particle production pair in a black hole is able to tunnel the gravitational barrier and escapes the black hole’s horizon. Thus, a black hole is not really black; it can radiate or evaporate particles [7]. The space-time having a black hole in it, first, has a singularity, and second, has a horizon preventing an external observer from seeing it. The singularity in GR is radically different from field theory singularities because it is a property not of some field but of the space-time itself. The topology of space-time is changed when it acquires a black hole [8].
The black hole possesses an event horizon (a one-way membrane) that casually isolates the inside of the black hole from the rest of the universe. The radius of the event horizon of spinning black holes given by the Schwarzschild radius can be obtained as eqn (1) [9]. Event horizons are mathematically simple consequences of Einstein’s general theory of relativity that were first pointed out by the German astronomer Karl Schwarzschild in a letter he wrote to Einstein in late 1915, less than a month after the publication of the theory. Quantum theory dictates that the event horizon must actually be transformed into a highly energetic region, or ‘firewall’, that would burn the astronaut to a crisp [10]. Now Hawking is suggesting a resolution to the paradox: Black holes do not possess event horizons after all, so they do not destroy information. Hawking says: “The absence of event horizons means that there are no black holes, in the sense of regimes from which light can’t escape.” In place of the event horizon, Hawking proposes that black holes possess “apparent horizons” that only temporarily entrap matter and energy that can eventually reemerge as radiation. This outgoing radiation possesses all the original information about what fell into the black hole, although in radically different form. Since the outgoing information is scrambled, Hawking writes, there’s no practical way to reconstruct anything that fell in based on what comes out [11]. Hawking’s new suggestion is that the apparent horizon is the real boundary [10], but the apparent horizon instead of the event horizon is a matter of discussion, so we consider the radius of event horizon of black holes.
                                    (1)
Hence the equation (1) can be transformed into the following equation.
                                    (2)
The above equation can be transformed into the energy of black holes as [5].
                                    (3)
Where EBHs=Mc2
                                    (4)
                                    (5)
The term is designated as black hole constant for the spinning black hole and may be defined with the help of eqn (3). For this putting in the equation (3) and we have,
                        EBHs=KBHs            (5)
Hence Black hole constant of the spinning black hole may be defined as the energy of the spinning black hole for unit radius of the event horizon.
This constant has the vital role of calculating the energy of different spinning black holes for the given radius of the event horizon. This constant may be also used to calculate the change in energy, internal energy, entropy, enthalpy and other thermodynamical parameters of black holes.
Data in the Support of the Mass and Energy of the Black Hole
There are two categories of black holes classified on the basis of their masses clearly very distinct from each other, with very different masses M ~ 520Ö¼ for stellar – mass black holes in X-ray binaries (XRBs) and M~106-109.5Ö¼ for super massive black holes in active galactic nuclei (AGN) [9,12,13]. Masses in the range 106Ö¼ to 3x109.5Ö¼ have been estimated by this means in about 20 galaxies [14] and other data in the support of mass of black holes in AGN can be seen in the research paper [14,15] and for energy of black hole in the research paper [16,17]. On the basis of the data available for the mass of black holes, we have calculated the energy of spinning black holes in XRBs and AGN for the given radius of event horizon listed in Tables 1 and 2 respectively.
Results and Discussion
In the present paper, we have calculated the energy of different spinning black holes existing in XRBs and AGN on the basis of model The calculation shows that the total energy for the rest masses (M) lying between 5Ö¼ to 20Ö¼ in XRBs is few×1055 ergs and for the rest masses (M) between 106Ö¼ to 109.5Ö¼ of super massive black holes in AGN is few×1060 −1064 ergs and agrees with the result of other research work done previously by Pacini and Salvati and by Krishan and justifies the validity of this model. The graphs have been plotted between: (i) the radius of event horizon of different spinning black holes and their corresponding energy in XRBs (Figure 1) (ii) the radius of event horizon of different spinning black holes and their corresponding energy in AGN (Figure 2).
Figures 1 and 2 obtained for XRBs and AGN are in a straight line showing the uniform variation between the radius of event horizon and their corresponding energy of spinning black holes. The straight line also shows that there is a linear relation between the radius of event horizon and energy of spinning black holes and justifies the validity of this model.
When the result of the present work is compared with the work in case of non-spinning black holes done by Mahto et al. [5], we observe that the energy of spinning black holes for the same mass is the exactly equal which shows that the energy of black holes depends only on mass, not on the spinning.
The two models for the energy of non-spinning and spinning black holes as proposed by Kanak et al. in 2010 and Mahto et al. [5] respectively also confirms the validity of Einstein’s mass-energy equivalence relation.
The discussion of present work requires the recent comments of Dr. Hawking on the non-existence of event horizon of black holes.
Conclusion
In the light of the present research work, we can draw the following conclusions:
1. There is a uniform variation between the radius of event horizon and energy of spinning black holes.
2. The straight line also shows that there is a definite relation between the radius of event horizon and the energy of spinning black holes and gives the validity of model as proposed by Mahto et al. [5].
3. The energy calculated on the basis of model agrees with the result of other research work done earlier by Pacini andSalvati (1982) and Krishan (1985), which also confirms the validity of model as proposed by Mahto et al. [5].
4. The larger the radius of event horizon, the greater is the energy of black holes and vice versa.
5. The energy of black holes depends only on mass, not on the spinning.
References

















Tables and Figures at a glance

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Table 1   Table 2

 

Figures at a glance

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Figure 1   Figure 2
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